Hypercomplex colour image processing

This page describes current work on hypercomplex processing of digital
colour images in the
Multimedia
Architectures and Applications Research Group in the
Department of Electronic Systems Engineering at the University of Essex.
The research described here was started at The University of Reading and
some details of related work completed at Reading are also
available.

Research on hypercomplex colour image processing started in 1996 and
arose from the work of Dr Amy Thornton
who applied complex Fourier transforms to chrominance images
(see here).
The quaternions are a generalization of the complex numbers
with an imaginary part consisting of three components, and the idea
was to use these to generalize techniques from signal and image processing,
such as frequency domain filtering and correlation, to handle colour
images as vector images.
More details about quaternions and links to general information elsewhere are
given on a separate page.

The first development, in 1996, was a quaternion Fast Fourier Transform
(FFT) based on the work of
Dr Todd A. Ell at the
University of Minnesota and published in 1993. Subsequently a collaboration
has developed and recently (June 2003) this collaboration has been supported
by the award of an EPSRC Visiting Fellowship (Grant no GR/S58621/01) valid
for 3 years.
In 1998, a new colour edge detector was developed using quaternion convolution.
The result of applying this edge detector to the Lena image is shown on a
separate page.

A significant development in the quaternion work is the definition of
auto-correlation and cross-correlation of colour images using quaternion
correlation. The following images show the results.

This work was presented in poster form at the IEEE International
Conference on Image Processing (ICIP99) in Kobe, Japan, in October
1999. The full paper is available in the conference proceedings
(IEEE copyright), and the poster is available here:

Publications

Sangwine, S. J. and Ell, T. A.,
'Mathematical approaches to linear vector filtering of color images',
First European Conference on Colour in Graphics, Imaging and Vision (CGIV 2002),
University of Poitiers, France, 2-5 April 2002,
The Society for Imaging Science and Technology, 348-351.

Hypercomplex Filtering of Digital Colour Images

This project is supported by EPSRC Grant GR/M45764,
and started in July 1999.
Dr Carolyn J. Evans
(now at CSIRO in Sydney) was the first Research
Fellow to work on this project (for about ten months, at the University of Reading).
From March 2001 until May 2002, Dr Eddie Moxey worked on the project, initially part-time,
but subsequently full-time. From September 2001, Dr Barnabas Gatsheni has been a second
Research Officer on the project.
The objective of the work is to develop new colour image filters based on
convolution using hypercomplex masks, and to understand the theory of
hypercomplex filtering. We have developed two new colour edge detecting
filters, published in conference papers, and we have also studied vector correlation.
We presented a poster at a one-day meeting held in London in January 2000 (available below).

Hypercomplex signal processing

Since 2001 a collaboration has developed with
Dr Nicolas le Bihan
at LIS, INPG, Grenoble. This collaboration is now supported by an EPSRC Visiting Fellowship (Grant
GR/S16881/01) valid for 2 years. The aim of the work is to extend hypercomplex matrix methods in
signal processing and image processing, including the singular value decomposition. Several
conference papers are already accepted and will be listed here shortly.